Myler converted before adding a penalty from a collapsed Glasgow scrum.
Glasgow prop Ryan Grant was then shown a yellow after 20 minutes for collapsing another scrum, before Myler added another three.
Russell added the extra two from distance, but Myler was to put the Saints 11 points ahead at the break as he added a kick between the posts following a penalty from the home side.
In the second half, Tuala added his second try of the match when he collected a handoff and powered over the line in the corner, but Myler was to miss the resulting conversion.
Luther Burrell was sent to the sin bin for the visitors, which allowed the Warriors to get back into the match when Strauss capitalised on his team's numerical advantage to cross the tryline.
However, the Saints proved to be determined in their defence to hold out for the victory, their second of the campaign.